The nonzero integers are closed under multiplication and contain the identity, but most elements have no inverse in the set: for example, the multiplicative inverse of $2$ is $1/2\notin\mathbb Z^*$. Hence $(\mathbb Z^*,\times)$ is not a group.


Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 302 / 1 / a / ii / Solution

 Solution (source code)